   Remark 3.4 
One crucial step for the proof of Proposition REF  is the estimate (REF ). To establish that, we have borrowed some interesting ideas in [1]}. In the above proof, we have imposed the element in \({B}\)  with a new equivalent norm in (REF ). This helps us bypass the using stochastic Fredholm integral equations, and simplify the arguments as in [2]} and [3]}. Such equivalent norm techniques also appeared in e.g. [4]}. However, we have to introduce more delicate arguments due to our quadratic growth framework.

